Minimal log discrepancies of hypersurface mirrors
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917576464924672 |
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| author | Esser, Louis |
| author_facet | Esser, Louis |
| contents | For certain quasismooth Calabi-Yau hypersurfaces in weighted projective space, the Berglund-Hübsch-Krawitz (BHK) mirror symmetry construction gives a concrete description of the mirror. We prove that the minimal log discrepancy of the quotient of such a hypersurface by its toric automorphism group is closely related to the weights and degree of the BHK mirror. As an application, we exhibit klt Calabi-Yau varieties with the smallest known minimal log discrepancy. We conjecture that these examples are optimal in every dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_13823 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Minimal log discrepancies of hypersurface mirrors Esser, Louis Algebraic Geometry 14J33 (primary), 14E30, 14J32, 14J40 (secondary) For certain quasismooth Calabi-Yau hypersurfaces in weighted projective space, the Berglund-Hübsch-Krawitz (BHK) mirror symmetry construction gives a concrete description of the mirror. We prove that the minimal log discrepancy of the quotient of such a hypersurface by its toric automorphism group is closely related to the weights and degree of the BHK mirror. As an application, we exhibit klt Calabi-Yau varieties with the smallest known minimal log discrepancy. We conjecture that these examples are optimal in every dimension. |
| title | Minimal log discrepancies of hypersurface mirrors |
| topic | Algebraic Geometry 14J33 (primary), 14E30, 14J32, 14J40 (secondary) |
| url | https://arxiv.org/abs/2304.13823 |